Home
Class 12
MATHS
The value of the integral int(0)^(pi)(1-...

The value of the integral `int_(0)^(pi)(1-|sin 8x|)dx` is

A

0

B

`pi-1`

C

`pi-2`

D

`pi-3`

Text Solution

Verified by Experts

The correct Answer is:
C
`I=int_(0)^(pi)1-|sin 8x|dx`
`= pi-int_(0)^(pi)(x|sin 8x|)dx`
`= pi-int_(0)^(8.(8)/(pi))(x|sin 8x|)dx`
`= pi-int_(0)^((8)/(pi))xsin 8xdx`
`=pi-8 [(- cos 8x)/(8)]^((pi)/(8)) `
`P+(-1-phi)=pi-2`
Promotional Banner

Topper's Solved these Questions

  • KVPY

    KVPY PREVIOUS YEAR|Exercise PART-2 MATHMATICS|10 Videos

  • KVPY

    KVPY PREVIOUS YEAR|Exercise Part 2 Mathematics|15 Videos

  • KVPY

    KVPY PREVIOUS YEAR|Exercise Part B- Mathematics|10 Videos

  • KVPY 2021

    KVPY PREVIOUS YEAR|Exercise PART II MATHEMATICS|4 Videos

Similar Questions

Explore conceptually related problems

The value of the integral int_(0)^(pi) | sin 2x| dx is

The value of the integral int_(0)^(pi)x log sin x dx is

The value of the integral int_(0) ^(pi//2) sin ^3 x dx is :

The value of integral int_(0)^( pi)xf(sin x)dx=

The value of the integral int_(0)^(pi//2) |sin x-cos x|dx , is

The value of the integral int_(0)^(pi//2) sin^(6) x dx , is

The value of the integral int _(0)^(pi//2) sin ^(5) x dx is

The value of the integral int_(a)^(a+pi/2)(|sin x|+|cos x|)dx, is

The value of the integral int_(0)^(pi) (sin k x)/(sin x)dx (k is an even integer) is equal to

The value of the integral int_(0)^((pi)/(2))(sin x)^(cos x)(cos x cot x-ln(sin x)^(sin x))dx

KVPY PREVIOUS YEAR-KVPY-PART-1 MATHEMATICS
  1. Suppose A=[{:(a,b),(c,d):}] is real matrix with nonzero entries, ad-b...

    Text Solution

    |

  2. On any given are of positive length on the unit circle |z|=1 in the co...

    Text Solution

    |

  3. For 0 lt theta lt (pi)/(2), four tangents are drawn at the four points...

    Text Solution

    |

  4. Let S ={x in R: cos(x)+cos(sqrt(2)x)lt2}. Then

    Text Solution

    |

  5. On a rectangular hyperbola x^(2)-y^(2)=a^(2),a gt 0, three points A,B,...

    Text Solution

    |

  6. The number of real solution x of the equation cos^(2)(x sin (2x))+(1...

    Text Solution

    |

  7. Let (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 , a gt b, be an ellipse with foc...

    Text Solution

    |

  8. Let a=cos 1^(@) and b= sin 1^(@). We say that a real number is algebra...

    Text Solution

    |

  9. A rectangle with its sides parallel to the x-axis and y-axis is inscib...

    Text Solution

    |

  10. Let f(x)=x|sin x|,x in R. Then

    Text Solution

    |

  11. Let f:[-1,1] to R be a function defined by f(x)={x^(2)|cos((pi)/(x))| ...

    Text Solution

    |

  12. The value of the integral int(0)^(pi)(1-|sin 8x|)dx is

    Text Solution

    |

  13. Let in x denote the logarithm of x with respect to the base e. Let S s...

    Text Solution

    |

  14. Let S be the set of real numbers p such that there is no nonzero conti...

    Text Solution

    |

  15. The porbability of men getting a certain disease is (1)/(2) and that o...

    Text Solution

    |

  16. The number of function f:[0,1] to [0,1]" satisfying " |f(x)-f(x)|=|x-...

    Text Solution

    |

  17. Suppose A is a 3xx3 matrix consisting of integer entries that are chos...

    Text Solution

    |

  18. Let X(k) be real number such that X(k)gtk^(4)+k^(2)+1 for 1 le k le 20...

    Text Solution

    |

  19. Let x^(2)=4ky,k gt 0 be a parabola with vertex A. Let BC be its latus ...

    Text Solution

    |

  20. Let f:[0'1] to [-1,1] and g:[-1,1] to [0,2] be two functions such that...

    Text Solution

    |